Algebra Examples

$\frac{x}{17} \geq 1 - \frac{x}{34}$

Step 1

Solve $x \geq \frac{34}{3}$ .

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Step 1.1

Multiply both sides by $17$ .

$\frac{x}{17} \cdot 17 \geq (1 - \frac{x}{34}) \cdot 17$

Step 1.2

Simplify.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Cancel the common factor of $17$ .

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Step 1.2.1.1.1

Cancel the common factor.

$\frac{x}{17} \cdot 17 \geq (1 - \frac{x}{34}) \cdot 17$

Step 1.2.1.1.2

Rewrite the expression.

$x \geq (1 - \frac{x}{34}) \cdot 17$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Simplify $(1 - \frac{x}{34}) \cdot 17$ .

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Step 1.2.2.1.1

Apply the distributive property.

$x \geq 1 \cdot 17 - \frac{x}{34} \cdot 17$

Step 1.2.2.1.2

Multiply $17$ by $1$ .

$x \geq 17 - \frac{x}{34} \cdot 17$

Step 1.2.2.1.3

Cancel the common factor of $17$ .

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Step 1.2.2.1.3.1

Move the leading negative in $- \frac{x}{34}$ into the numerator.

$x \geq 17 + \frac{- x}{34} \cdot 17$

Step 1.2.2.1.3.2

Factor $17$ out of $34$ .

$x \geq 17 + \frac{- x}{17 (2)} \cdot 17$

Step 1.2.2.1.3.3

Cancel the common factor.

$x \geq 17 + \frac{- x}{17 \cdot 2} \cdot 17$

Step 1.2.2.1.3.4

Rewrite the expression.

$x \geq 17 + \frac{- x}{2}$

Step 1.2.2.1.4

Simplify the expression.

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Step 1.2.2.1.4.1

Move the negative in front of the fraction.

$x \geq 17 - \frac{x}{2}$

Step 1.2.2.1.4.2

Reorder $17$ and $- \frac{x}{2}$ .

$x \geq - \frac{x}{2} + 17$

Step 1.3

Solve for $x$ .

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Step 1.3.1

Move all terms containing $x$ to the left side of the inequality.

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Step 1.3.1.1

Add $\frac{x}{2}$ to both sides of the inequality.

$x + \frac{x}{2} \geq 17$

Step 1.3.1.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x \cdot \frac{2}{2} + \frac{x}{2} \geq 17$

Step 1.3.1.3

Combine $x$ and $\frac{2}{2}$ .

$\frac{x \cdot 2}{2} + \frac{x}{2} \geq 17$

Step 1.3.1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x}{2} \geq 17$

Step 1.3.1.5

Simplify the numerator.

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Step 1.3.1.5.1

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + x}{2} \geq 17$

Step 1.3.1.5.2

Add $2 x$ and $x$ .

$\frac{3 x}{2} \geq 17$

Step 1.3.2

Multiply both sides by $2$ .

$\frac{3 x}{2} \cdot 2 \geq 17 \cdot 2$

Step 1.3.3

Simplify.

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Step 1.3.3.1

Simplify the left side.

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Step 1.3.3.1.1

Cancel the common factor of $2$ .

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Step 1.3.3.1.1.1

Cancel the common factor.

$\frac{3 x}{2} \cdot 2 \geq 17 \cdot 2$

Step 1.3.3.1.1.2

Rewrite the expression.

$3 x \geq 17 \cdot 2$

Step 1.3.3.2

Simplify the right side.

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Step 1.3.3.2.1

Multiply $17$ by $2$ .

$3 x \geq 34$

Step 1.3.4

Divide each term in $3 x \geq 34$ by $3$ and simplify.

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Step 1.3.4.1

Divide each term in $3 x \geq 34$ by $3$ .

$\frac{3 x}{3} \geq \frac{34}{3}$

Step 1.3.4.2

Simplify the left side.

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Step 1.3.4.2.1

Cancel the common factor of $3$ .

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Step 1.3.4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{34}{3}$

Step 1.3.4.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{34}{3}$

Step 2

Use the inequality $x \geq \frac{34}{3}$ to build the set notation.

${x | x \geq \frac{34}{3}}$

Step 3